JEE Mains · Maths · STD 11 - 7. binomial theoram
The sum of all rational terms in the expansion of \(\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}\) is equal to :
- A \(3133\)
- B \(633\)
- C \(931\)
- D \(6131\)
Answer & Solution
Correct Answer
(A) \(3133\)
Step-by-step Solution
Detailed explanation
\( \mathrm{T}_{\mathrm{r}+1}={ }^{15} \mathrm{C}_{\mathrm{r}}\left(5^{\frac{1}{3}}\right)^{\mathrm{r}}\left(2^{\frac{1}{5}}\right)^{15-\mathrm{r}} \) \( ={ }^{15} \mathrm{C}_{\mathrm{r}} 5^{\frac{\mathrm{r}}{3}} \cdot 2^{\frac{15-\mathrm{r}}{5}} \)…
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